Fenchel-Rockafellar Theorem in Infinite Dimensions via Generalized Relative Interiors

Abstract: In this paper we provide further studies of the Fenchel duality theory in the general frame work of locally convex topological vector (LCTV) spaces. We prove the validity of the Fenchel strong duality under some qualification conditions via generalized relative interiors imposed on the epigraphs and the domains of the functions involved. Our results directly generalize the classical Fenchel-Rockafellar theorem on strong duality from finite dimensions to LCTV spaces.